Pairwise comparison facts for kids

Pairwise comparison is a way of comparing two things at a time. You do this to decide which one you like more, which one has more of something, or if they are exactly the same. Scientists and people who study how we make choices use this method. It helps them understand what people prefer, how voting systems work, and even how smart computer systems (AI) make decisions. In psychology (the study of the mind), it's often called paired comparison.

How We Compare Things

Imagine you have two choices, let's call them x and y. When you compare them, you can show what you prefer. There are three main ways you can compare them:

• You like x more than y. This can be written as "x > y" or "xPy".
• You like y more than x. This can be written as "y > x" or "yPx".
• You don't have a favorite between x and y. This means you are "indifferent" to them. It can be written as "x = y" or "xIy".

What is Transitivity?

When we make comparisons, we usually expect them to follow a rule called transitivity. This means our preferences should make sense in a chain.

Think of it like this:

• If you like x more than y, AND you like y more than z, then it makes sense that you should like x more than z. This is a transitive preference.

Here are the main rules for transitivity:

• If you prefer x over y (xPy), and you prefer y over z (yPz), then you should prefer x over z (xPz).
• If you prefer x over y (xPy), and you are indifferent between y and z (yIz), then you should prefer x over z (xPz).
• If you are indifferent between x and y (xIy), and you prefer y over z (yPz), then you should prefer x over z (xPz).
• If you are indifferent between x and y (xIy), and you are indifferent between y and z (yIz), then you should be indifferent between x and z (xIz).

When Indifference Isn't Transitive

Sometimes, being "indifferent" (not having a preference) might not follow the transitivity rule. Let's look at an example with apples:

Imagine you like bigger apples. You have three apples: Apple A, Apple B, and Apple C.

• Apple B is just a tiny bit bigger than Apple A. You can't tell the difference just by looking.
• Apple C is just a tiny bit bigger than Apple B. Again, you can't tell the difference by looking.
• But, Apple C is noticeably bigger than Apple A. You can easily see this difference.

When you compare them in pairs without a special measuring tool:

• You are shown Apple A and Apple B. Since you can't see the tiny difference, you feel no preference. You are indifferent.
• You are shown Apple B and Apple C. Again, you can't see the tiny difference, so you are indifferent.
• However, when you are shown Apple A and Apple C, you can clearly see that C is bigger. So, you prefer Apple C over Apple A.

In this example, even though you were indifferent between A and B, and indifferent between B and C, you were NOT indifferent between A and C. This shows how indifference might not always be transitive.

Related pages

• Analytic Hierarchy Process
• Law of comparative judgment
• Potentially all pairwise rankings of all possible alternatives (PAPRIKA) method
• PROMETHEE pairwise comparison method
• Preference (economics)
• Stochastic Transitivity
• Condorcet method

See also

In Spanish: Comparación por pares para niños